$2.70 vs $5.50 Super Turbo

    • Styr
      Styr
      Silver
      Joined: 11.03.2009 Posts: 410
      This does not concern SNG strategy, but I thought it is relevant nonetheless.

      I have been playing both $2.70 and $5.50 54-man Super Turbo SNG's at Full Tilt, and have observed, that over all the games I have played, I have enjoyed a significantly better ROI from the $5.50 tournaments. I might play several $2.70 ones to even get close to the money, and a few more to actually win one, whereas I have won, or placed in the top three of most of the $5.50 ones I have played.

      I admit, I have not put a huge volume into those, but I thought it should be the other way round, if there should even be such a discrepancy.

      Has anybody else noticed something along those lines? Or is it just a short term variation?
  • 7 replies
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      My guess is that it is a short-term variation. It takes a very long time for your ROI to converge.

      While it is possible for a higher rake at lower levels to make it harder to win, usually the greater concentration of casual players mean that it is easier to beat lower stakes games.

      Your true ROI will be within a 95% confidence interval 95% of the time. The width of a 95% confidence interval does not depend much on your playing style when you play STTs, but it does depend a bit when you play MTTs. It is also wider if you play larger MTTs.

      For 54-player SNGs, a 95% confidence interval after n tournaments may be your observed ROI +- 600%/squareroot(n). (With some styles, the 600% would be a little higher.) If you have played 400 tournaments with an ROI of 50%, then a 95% confidence interval would be 50% +- 600%/sqrt(400) = 50% +- 30%, or from 20% to 80%. At that point, you would be confident that you are winning, but you don't really know by how much.

      For STTs, a 95% confidence interval is about the observed ROI +- 310%/sqrt(n).

      When you are trying to compare two levels, you can compute the difference between your ROIs at the two levels. The width of the confidence interval for the difference is related to the confidence intervals for each level by the Pythagorean formula, Sqrt(A^2 + B^2). For example, if your confidence intervals for your ROIs are 10%+-20% and 50%+-30%, then the confidence interval for the difference is (50-10)+-sqrt(20^2+30^2) ~ 40 +- 36%.
    • Hlynkinn
      Hlynkinn
      Bronze
      Joined: 14.06.2008 Posts: 4,998
      you really made a formula for calculating confidence?
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      The confidence interval is a standard tool in statistics. The ingredient needed to apply them to SNGs is the standard deviation, which is about 1.55 buy-ins (155%) per tournament for 9-player tournaments, and about twice as much for 54-player tournaments.

      The standard deviation of your average result in n tournaments is your standard deviation for one tournament divided by sqrt(n).

      A rough 95% confidence interval is +- 2 standard deviations, so +- 2x155%/sqrt(n) for 9-player tournaments.
    • nibbana
      nibbana
      Bronze
      Joined: 04.12.2009 Posts: 1,186
      Do you know how these calculations change for 6max and HU sng's pzhon ?

      EDIT - and anywhere I can find out how 155% was reached for 9man !?
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      The easiest is for HU SNGs. The standard deviation is just under 1 buy-in per tournament. In a sense, a gamble is about as risky as a fair coin-flip for 1 standard deviation. A double-or-nothing tournament or a HUSNG is close to a coin-flip for 1 buy-in. Because of the rake, and that you might win more than 50%, the standard deviation may be a little lower, perhaps 0.95 buy-ins per tournament.

      For 6-max tournament, the standard deviation depends on the prize structure. Flatter structures have lower standard deviations. There are DoN and 50-30-20 6-max tournaments as well as 60-40, 65-35, and 70-30 structures.

      To estimate your standard deviation, a shortcut is to subtract the square of the average result from the average square result. This gives you the mathematical variance. The square root of that is the standard deviation.

      Example: You play $12+1 6-max tournaments with a 65-35 structure. You place first 20% and second 18%.

      Avg result: 0.20 x $46.80 + 0.18 x $25.20 = $13.90
      Avg square result: 0.20 x (46.80^2) + 0.18 x (25.20)^2 = 552.355
      Variance: 552.355 - 13.90^2 = 359.256
      Standard deviation: sqrt(359.256) = $18.95 = 1.46 buy-ins.

      This figure changes a little if you have a different reasonable finish distribution, but not by much. When you play STTs, the standard deviation primarily depends on the prize structure, not your playing style. So, you can compute the standard deviation assuming that you finish in each place equally often. For MTTs, a high skill level may increase your variance significantly, as might a playing style which aims for the top 3, sacrificing many lower finishes to try to accumulate a big stack.
    • santostr
      santostr
      Bronze
      Joined: 11.08.2009 Posts: 663
      Originally posted by pzhon
      For STTs, a 95% confidence interval is about the observed ROI +- 310%/sqrt(n).
      So, this means you need 96K STT to get a reliable +-1% interval?

      Soooo sick...
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      Yes, it would take about a hundred thousand STTs to be confident of your ROI to within 1% from your results alone. All-in luck adjustment might remove 55-60% of the variance, so that it would only take about 40 thousand STTs. However, usually you don't need to know your ROI within 1% with high confidence. Also, even after you only play 40k games, the games will have changed.